Invariant measures for the defocusing Nonlinear Schrödinger equation
[Mesures invariantes pour l’équation de Schrödinger non linéaire]
Tzvetkov, Nikolay1
1 Université Lille I Département de Mathématiques 59 655 Villeneuve d’Ascq Cedex (France)
Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2543-2604.

On démontre l’existence et l’invariance d’une mesure de Gibbs par le flot de l’équation de Schrödinger non linéaire posée sur le disque du plan ℝ 2 . On démontre également une estimée qui donne une idée de ce qui pourrait arriver en dimension 3.

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane ℝ 2 . We also prove an estimate giving some intuition to what may happen in 3 dimensions.

DOI : 10.5802/aif.2422
Classification : 35Q55, 35BXX, 37K05, 37L50, 81Q20
Keywords: Nonlinear Schrödinger, eigenfunctions, dispersive equations, invariant measures
Mot clés : Equation de Schrödinger non linéaire, fonctions propres, équations dispersives, mesures invariantes
Tzvetkov, Nikolay 1

1 Université Lille I Département de Mathématiques 59 655 Villeneuve d’Ascq Cedex (France) 
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     title = {Invariant measures for the defocusing {Nonlinear} {Schr\"odinger} equation},
     journal = {Annales de l'Institut Fourier},
     pages = {2543--2604},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {58},
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Tzvetkov, Nikolay. Invariant measures for the defocusing Nonlinear Schrödinger equation. Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2543-2604. doi : 10.5802/aif.2422. http://www.numdam.org/articles/10.5802/aif.2422/

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